Question

If y=x^(x+y) , find f'(x).
work/explanation would be nice

Answer 1

I think it will be better if you take the ln of both sides.
lny = lnx^(x+y)

Answer 2

Then, it will become
lny = (x+y) lnx

Answer 3

Then do the implicit differentiation, do you know that @BasicalyBrandon